Figure 1

Schematic illustration for the three single-qutrit three-party communication protocols. Alice prepares state $|\mathit{\psi }〉$, Alice, Bob and Charlie act with the operation UⁱV^j sequentially on the received state according to their input data (i, j), where (i, j) are (a₀, a₁), (b₀, b₁) and (c₀, c₁) for Alice, Bob and Charlie, respectively. Finally, Charlie performs a measurement on the qutrit in the Fourier basis.